An HR manager of DataCom uses regression analysis to predict employees' salaries. Data for 46 randomly selected employees have been collected. In addition to the salary (Y), the variables measured years of previous working experience, years employed, years of education, gender, and department. Here is part of thedataset.

Previous working experience is measured by the number of years of this employee's relevant working experience before coming to DataCom. "Years employed" means the number of years employed at DataCom. Years of education mean the years of education beyond high school. Gender is coded as 0 for female and 1 for male. The "NumberSupervised" means the number of employees supervised by this employee. The variable of department here includes four different departments: 1=Sales, 2=Purchasing, 3=Advertising, 4=Engineering. In order to run the regression, the HR manager has recoded the department into three dummy variables, and department four is the reference department.

1. Based on the multiple regression output, please write the complete multiple regression equation to predict salary in DataCom (3 points).

2. How well does the regression equation fit the given data (5 points)?

3. Interpret the estimated regression coefficients of "Years Employed," "Years Education," Gender and Department (12 points).

4. Interpret the ANOVA table for this model. In particular, does this set of independent variables provide at least some power in explaining the variation in Salary (5 points)? (hint: report F statistics and p-value)

5. Does the independent variable "NumberSupervised" have a significant effect on salary at the 5% significant level (5 points)?

6. Using the regression output, determine which of the independent variables could be excluded from the regression equation. Justify your choices (5 points). (Pay attention to the numbers of p values. If a p-value includes an "E," that means the p-value is very small and close to 0).